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Given b=2,c=sqrt3and A= 30^@, then in-ra...

Given b=2,c=`sqrt3`and A= `30^@,` then in-radius of triangle ABC is

A

`(sqrt3 -1)/(2)`

B

`(sqrt3 + 1)/(2)`

C

`(sqrt3-1)/(4)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`b = 2, c = sqrt3, anlge A = 30^(@)`
`a = sqrt(b^(2) + c^(2) - 2bc cos A)`
`= sqrt(4+3 - 2 xx 2 sqrt3 (sqrt3)/(2)) = 1`
`rArr r = (s-a) tan.(A)/(2)`
`= (b + c-a)/(2) tan.(A)/(2)`
`= (sqrt3 +1)/(2) tan 15^(@)`
`= (sqrt3 +1)/(2) (sqrt3 -1)/(sqrt3+1) = (sqrt3 -1)/(2)`
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